Bob-
Take 225/40R18
225=width of tire in mm.
40 is not the direct measurement of the sidewall of the tire, but relates to the sidewall in that it is an aspect ratio comparing sidewall to tire width. My sidewall is 40% of 225mm...basically smaller the number, thinner the sidewall (more low-profile)
R=Radial
18=wheel diameter (measured from where the tire contacts the smallest outer circumference)

I'm sure www.discounttire.com and www.tirerack.com have some explanations if you want more info.